%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM464+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:18 PM UTC 2026
% Result : Theorem 2.69s 1.33s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 13 unt; 3 def)
% Number of atoms : 103 ( 32 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 107 ( 46 ~; 40 |; 15 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(f26,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sz00
| X0 = sz10
| ( sz10 != X0
& sdtlseqdt0(sz10,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLENTr) ).
fof(f27,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__987) ).
fof(f28,conjecture,
( xm != sz00
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sz10,X0) = xm )
| sdtlseqdt0(sz10,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f29,negated_conjecture,
~ ( xm != sz00
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sz10,X0) = xm )
| sdtlseqdt0(sz10,xm) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f31,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xm != sdtpldt0(sz10,X0) )
& ~ sdtlseqdt0(sz10,xm)
& xm != sz00 ),
inference(ennf_transformation,[],[f29]) ).
fof(f32,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xm != sdtpldt0(sz10,X0) )
& ~ sdtlseqdt0(sz10,xm)
& xm != sz00 ),
inference(flattening,[],[f31]) ).
fof(f36,plain,
! [X0] :
( X0 = sz00
| X0 = sz10
| ( sz10 != X0
& sdtlseqdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f37,plain,
! [X0] :
( X0 = sz00
| X0 = sz10
| ( sz10 != X0
& sdtlseqdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f36]) ).
fof(f41,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f42,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f41]) ).
fof(f62,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f27]) ).
fof(f63,plain,
sz00 != xm,
inference(cnf_transformation,[],[f32]) ).
fof(f64,plain,
~ sdtlseqdt0(sz10,xm),
inference(cnf_transformation,[],[f32]) ).
fof(f71,plain,
! [X0] :
( sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f76,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f81,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f96,definition,
~ sP2(sz00),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f97,plain,
sP2(xm),
inference(inequality_splitting,[],[f63,f96]) ).
fof(f109,plain,
( sz10 = xm
| sz00 = xm
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f64,f71]) ).
fof(f110,plain,
( sdtlseqdt0(xm,sz10)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[],[f64,f81]) ).
fof(f112,plain,
( sdtlseqdt0(xm,sz10)
| ~ aNaturalNumber0(sz10) ),
inference(forward_subsumption_resolution,[],[f110,f62]) ).
fof(f113,plain,
( sz10 = xm
| sz00 = xm ),
inference(forward_subsumption_resolution,[],[f109,f62]) ).
fof(f114,plain,
sdtlseqdt0(xm,sz10),
inference(forward_subsumption_resolution,[],[f112,f76]) ).
fof(f116,definition,
( spl7_1
<=> sz00 = xm ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f118,plain,
( sz00 = xm
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f120,definition,
( spl7_2
<=> sz10 = xm ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f122,plain,
( sz10 = xm
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f113,f120,f116]) ).
fof(f144,plain,
( sdtlseqdt0(sz10,sz10)
| ~ spl7_2 ),
inference(superposition,[],[f114,f122]) ).
fof(f145,plain,
( ~ sdtlseqdt0(sz10,sz10)
| ~ spl7_2 ),
inference(superposition,[],[f64,f122]) ).
fof(f150,plain,
( $false
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f144,f145]) ).
fof(f151,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[],[f150]) ).
fof(f158,plain,
( sP2(sz00)
| ~ spl7_1 ),
inference(superposition,[],[f97,f118]) ).
fof(f160,plain,
( $false
| ~ spl7_1 ),
inference(forward_subsumption_resolution,[],[f158,f96]) ).
fof(f161,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[],[f160]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f123]) ).
cnf(s3,plain,
~ spl7_2,
inference(sat_conversion,[],[f151]) ).
cnf(s4,plain,
~ spl7_1,
inference(sat_conversion,[],[f161]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
fof(f162,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM464+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 19:59:40 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.69/1.33 % (1746514)Detected formulas, will run a generic FOF schedule.
% 2.69/1.33 % (1746522)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2244512194:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.33 % (1746522)First to succeed.
% 2.69/1.33 % (1746522)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1746514"
% 2.69/1.33 % (1746521)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2233435209:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.33 % (1746525)dis-21_1_sil=8000:lcm=predicate:random_seed=1139635454:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.69/1.33 % (1746523)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3456470558:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.33 % (1746520)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2278583196:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.33 % (1746519)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3530345983:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.33 % (1746524)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3866448721:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.33 % (1746523)Also succeeded, but the first one will report.
% 2.69/1.33 % (1746524)Also succeeded, but the first one will report.
% 2.69/1.33 % (1746525)Instruction limit reached!
% 2.69/1.33 % (1746525)------------------------------
% 2.69/1.33 % (1746525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.33 % (1746525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.33 % (1746525)CaDiCaL version: 2.1.3
% 2.69/1.33 % (1746525)Termination reason: Instruction limit
% 2.69/1.33 % (1746525)Termination phase: Saturation
% 2.69/1.33 % (1746525)Time elapsed: 0.081 s
% 2.69/1.33 % (1746525)Peak memory usage: 90 MB
% 2.69/1.33 % (1746525)Instructions burned: 129 (million)
% 2.69/1.33 % (1746522)Refutation found. Thanks to Tanya!
% 2.69/1.33 % SZS status Theorem for theBenchmark
% 2.69/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.33 % (1746522)------------------------------
% 2.69/1.33 % (1746522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.33 % (1746522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.33 % (1746522)CaDiCaL version: 2.1.3
% 2.69/1.33 % (1746522)Termination reason: Refutation
% 2.69/1.33 % (1746522)Time elapsed: 0.003 s
% 2.69/1.33 % (1746522)Peak memory usage: 89 MB
% 2.69/1.33 % (1746522)Instructions burned: 4 (million)
% 2.69/1.33 % (1746522)------------------------------
% 2.69/1.33 % (1746522)------------------------------
% 2.69/1.33 % (1746514)Success in time 0.301 s
% 2.69/1.33 % Vampire exiting
%------------------------------------------------------------------------------